mathematic

From a math point of view, a scalar is something that is one dimensional, while a vector is something with more than one (usually two or three) dimensions. There are rules for combining them. For example, scalars use ordinary arithmetic. Addition or subtraction of vectors is straightforward but multiplication is more complicated.

log has discontinuity at 0. arc ? - what do you mean?

Graduate school is always a good idea. You need to factor personal needs, such as money, your age.

Without fiction you can ignore the horizontal motion. You need to start with the vertical component of velocity and use the usual formula for gravity acceleration.

Why not? Change a system and it will go to new equilibrium - determined by stat. mech.

Second law is statistical.. It is possible for something weird to happen, but the probability is astronomically small.

Real world complication example: how willing the buyer is willing to pay a given price will strongly correlate how well the care is running.

Another approach cos(x)=sin(90-x), so cos(90)=sin(0). In a right triangle, it is obvious sin(0)=0.

You have assumed the buyer's "satisfactions" are independent, which may not be true.

Question seems premature. Exomoons have yet to be discovered. The description of habitable applies just as well to exoplanets.

Are you asking permission to discuss your idea? If so, you have my blessing.

The statement is a little confusing. I believe its intent was to consider only those values of X which have a probability greater than zero. Simple example: X has 3 values 0,1,-1. f(-1)=1/4, f(0)=1/2, and f(1)= 1/4. g(-1)=0, g(0)=1, g(1)=2. Then E(g(X))=1.

ARPA contribution was setting up the network. I presume, based on your reference, that ASCII was the code used in transmission. At that time IBM had a competing code called EBCDIC. I don't know the subsequent history.

My recollection is that the beginnings of the internet idea was developed by ARPA (now DARPA) around 1960 or so. Their version involved connecting various science research computer facilities and included remote access by outsiders.

Formula (trouble with LaTex) B(x,y)=G(x)G(y)/G(x+y), G=gamma, B=Beta

As long as there is Oxygen around it will catch fire, once it is hot enough. On a hot sunny day, you could start a fire with paper and a magnifying glass.

I'm not absolutely sure, but I believe the time distribution for decay is exponential.

In a world consisting of anti-matter, moving positrons would be electricity.

I suspect food production will continue.

There is a standard procedure to calculate the determinant of a 3x3 matrix.

So far to date, string theory etc. has no experimental basis. The basic problem is reconciling quantum theory and general relativity when both are needed (black holes).

You have given a sequence of sentences??????

If the universe is like a torus, then it has to be very big to look flat locally.

Within a galaxy, it is impossible for anything to be stationary - gravity!

The concept of sequence is well defined - a set which is 1-1 with integers (all or part). What is being described are sets which are not necessarily sequences.